excess being most pronounced since 1887; (4) Analysis, "which takes
its rise equally from calculus, from the algebra of imaginaries, from
the intuitions and the critically refined developments of geometry, and
from abstract logic: the common servant and chief ruler of the other
branches of mathematics," shows a trebling in forty years, reaching
its first maximum in 1890, "probably the culmination of waves set
in motion by Weierstrassand Fuchsin Berlin, by Riemannin Göt-
tingen, by Hermitein Paris, Mittag-Lefflerin Stockholm, Diniand
Brioschiin Italy ;" before 1887much of the growth of analysis is due
to the theory of functions which reaches a maximum about 1887,
with a sweep of the curve upward again after 1900, due to the theory
of integral equations and the influence of Hilbert; (5) Algebra, in-
cluding series and groups, experienced during the forty years a steady
gain to 2½ times its original output; the part of algebra relating to
algebraic forms, invariants, etc., reached its acme before 1890and
then declined most surprisingly; (6) Differential equations increased
in amount slowly but steadily from 1870, "under the combined in-
fluence of Weierstrass, Darbouxand Lie," showing a slight decline
in 1886, but "followed by a marked recovery and advance during the
publication of lectures by Forsyth, Picard, Goursatand Painlevé;"
(7) The mathematical theory of electricity and magnetism remained
less than one-fourth of the whole applied mathematics, but rose after
1873steadily toward one-fourth, by the labors of Clerk Maxwell,
W. Thomson( Lord Kelvin) and P. G. Tait; (8) The constant shifting
of mathematical investigation is due partly to fashion.

The progress of mathematics has been greatly accelerated by the
organization of mathematical societies issuing regular periodicals.
The leading societies are as follows: London Mathematical Society
organized in 1865, La société mathématique de Franceorganized in
1872, Edinburgh Mathematical Societyorganized 1883, Circolo mate-
matico di Palermoorganized in 1884, American Mathematical Society
organized in 1888under the name of New York Mathematical Society
and changed to its present name in 1894, ¹ Deutsche Mathematiker-
Veieinigungorganized in 1890, Indian Mathematical Societyorganized
in 1907, Sociedad Metematica Espaholaorganized in 1911, Mathematical
Association of Americaorganized in 1915.

The number of mathematical periodicals has enormously increased
during the passed century. According to Felix Müller ² there were,
up to 1700, only 17 periodicals containing mathematical articles;
there were, in the eighteenth century, 210 such periodicals, in the
nineteenth century950 of them.

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